Characterising discs around Herbig Ae/Be stars through modelling of low-J $^{12}$CO lines

Context. While there has been extensive investigation of the dust emission in discs around young intermediate-mass or Herbig Ae/Be stars at a range of wavelengths, their gas content has been systematically studied mainly via spatially unresolved (sub)millimetre observations of the rotational lines of 12 CO. Aims. We are interested in how the available low-J 12 CO spectra compare to the disc properties inferred from the dust emission, and to what extent the gas- and dust-emission approaches to disc modelling are complementary to each other. Methods. First, we use the disc structure derived from the spectral energy distribution (SED) modelling to produce the synthetic 12 CO J = 3−2 spectra for a discrete sample of sources. We then compare these synthetic spectra to observations, to test the existing disc models for each source. In our second approach, we study the dependence of the 12 CO J = 3−2 spectrum on disc size, inclination and temperature, for discs around Herbig Ae/Be stars in general. We calculate the spectral line profiles for a grid of parametric disc models. The calculated spectra are compared to the spectra observed towards a large sample of sources. Both methods use a molecular excitation and radiative transfer code for the calculation of the 12 CO line emission. Results. SED models are insensitive to the parameters that dominate the low-J 12 CO emission, i.e., the disc size and orientation. To minimise some of the important parameter degeneracies, it is necessary to model a disc’s SED with prior knowledge of the disc size and inclination. We show how the spectral profile of low-J 12 CO lines can be used to constrain these parameters, and to obtain disc models that are good starting points for the outside-in SED modelling of discs from long to shorter wavelengths. Conclusions. For a disc gas mass of the order of 0.01 M� , the optically thick J = 3−2 12 CO line intensity shows that the majority of discs around Herbig Ae/Be stars are smaller than 200 AU, and that the largest and brightest sources thoroughly studied with submillimetre interferometry are not representative of the sample.